Some Types of Generalized Fuzzyn-Fold Filters in Residuated Lattices

Abstract

Fuzzy filters and their generalized types have been extensively studied in the literature. In this paper, a one-to-one correspondence between the set of all generalized fuzzy filters and the set of all generalized fuzzy congruences is established, a quotient residuated lattice with respect to generalized fuzzy filter is induced, and several types of generalized fuzzyn-fold filters such as generalized fuzzyn-fold positive implicative (fantastic and Boolean) filters are introduced; examples and results are provided to demonstrate the relations among these filters.

Fuzzyn-Fold Filters of Pseudoresiduated Lattices

“…In the fuzzy approach, a lot of work has been done on fuzzy filters which are particular cases of fuzzy sets introduced by Zadeh [10] (a fuzzy subset of a set is a map : → , where := [0; 1] is the closed unit interval of real numbers); most of the authors (see, e.g., [11][12][13][14][15][16][17][18][19][20][21][22]) use the above original definition of a fuzzy subset.…”